Transformation of the discrete stable process via branching reproduction environment (2503.23180v1)

Abstract: The current paper focuses on studying the impact of immigration with an infinite mean, driven by a discrete-stable compound Poisson process, when it is entering the branching environment with infinite variance of reproduction. Our goal is to determine the explicit form of the probability generating function and subsequently to analyze the probability of extinction, aiming to understand the long-term behavior of such processes.